Branching rules for level-zero extremal weight modules from U_q(\widehat\mathfraksl_n+1) to U_q(\widehat\mathfraksl_n)

2025/01/20 by Shutaro Nakaoka, Nakaoka, Shutaro
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2501.11559

openalex publication_date 2025/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the structure of a U_q(\widehat\mathfraksl_n)-module Ψ_ε^* V(λ), where V(λ) is the extremal weight module of level-zero dominant weight λ over the quantum affine algebra U_q(\widehat\mathfraksl_n+1) and Ψ_ε: U_q(\widehat\mathfraksl_n) → U_q(\widehat\mathfraksl_n+1) is an injective algebra homomorphism. We establish a direct sum decomposition Ψ_ε^* V(λ) ≅ M_0,ε ⊕ ⋯ ⊕ M_m,ε, where M_0,ε and M_m,ε are isomorphic to a tensor product of an extremal weight module over U_q(\widehat\mathfraksl_n) and a symmetric Laurent polynomial ring. Moreover, when λ is a multiple of a level-zero fundamental weight, we show that Ψ_ε^* V(λ) is isomorphic to a direct sum of extremal weight modules.

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